Numerical Experiment with the Construction of a Control Operator Applied in ECGM Algorithm

Felix Makanjuola Aderibigbe; Bosede Ojo; Kayode James Adebayo

doi:doi:10.11648/j.ajam.20150301.13

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Numerical Experiment with the Construction of a Control Operator Applied in ECGM Algorithm

Felix Makanjuola Aderibigbe, Bosede Ojo, Kayode James Adebayo

Published in American Journal of Applied Mathematics (Volume 3, Issue 1)

Received: 25 December 2014 Accepted: 10 January 2015 Published: 20 January 2015

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Abstract

In this paper, we constructed a control operator, G, which enables an Extended Conjugate Gradient Method (ECGM) to be employed in solving for the optimal control and trajectories of continuous time linear regulator problems. Similar operators constructed in the past by various authors have limited application. This call for the construction of the control operator that is aimed at taking care of any of the Mayer’s, Lagrange’s and Bolza’s cost form of linear regulator problems. The authors of this paper desire that, with the construction of the operator, one will circumvent the difficulties undergone using the classical methods and its application will further improve the result of the Extended Conjugate Gradient Method in solving this class of optimal control problem. The constructed Linear Control Operator is applied in ECGM algorithm to solve Continuous-Time Linear Regulator Problems with the convergence profile showing the efficiency of the operator.

Published in	American Journal of Applied Mathematics (Volume 3, Issue 1)
DOI	10.11648/j.ajam.20150301.13
Page(s)	8-13
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Continuous Linear Regulator Problem, Control Operator, Extended Conjugate Gradient Method, Optimal Control

References

[1]	Athans, M. and Falb, P. L., (1966), Optimal Control: An Introduction to the Theory and Its Applications, McGraw-Hill, New York.
[2]	Aderibigbe, F. M., (1993), “An Extended Conjugate Gradient Method Algorithm for Control Systems with Delay-I”, Advances in Modeling & Analysis, C, AMSE Press, Vol. 36, No. 3, pp 51-64.
[3]	George M. Siouris, (1996), An Engineering Approach To Optimal Control And Estimation Theory, John Wiley & Sons, Inc., 605 Third Avenue, New York, 10158-00 12.
[4]	Hasdorff, L. (1976), Gradient optimization and Nonlinear Control. J. Wiley and Sons, New York.
[5]	Ibiejugba, M. R. and Onumanyi, P., (1984), “A Control Operator and some of its Applications, J. Math. Anal. Appl. Vol. 103, No. 1. Pp. 31-47.
[6]	David, G. Hull, (2003), Optimal Control Theory for Applications, Mechanical Engineering Series, Springer-Verlag, New York, Inc., 175 Fifth Avenue, New York, NY 10010.
[7]	Gelfand, I. M. and Fomin, S. V., (1963), Calculus of Variations, Patience Hall, Inc., New Jersey.
[8]	George, F. Simmons, (1963), Introduction to Topology and Modern Analysis, McGraw- Hill Kogakusha, Book Company, Inc., Tokyo, Japan.

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APA Style

Felix Makanjuola Aderibigbe, Bosede Ojo, Kayode James Adebayo. (2015). Numerical Experiment with the Construction of a Control Operator Applied in ECGM Algorithm. American Journal of Applied Mathematics, 3(1), 8-13. https://doi.org/10.11648/j.ajam.20150301.13

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ACS Style

Felix Makanjuola Aderibigbe; Bosede Ojo; Kayode James Adebayo. Numerical Experiment with the Construction of a Control Operator Applied in ECGM Algorithm. Am. J. Appl. Math. 2015, 3(1), 8-13. doi: 10.11648/j.ajam.20150301.13

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AMA Style

Felix Makanjuola Aderibigbe, Bosede Ojo, Kayode James Adebayo. Numerical Experiment with the Construction of a Control Operator Applied in ECGM Algorithm. Am J Appl Math. 2015;3(1):8-13. doi: 10.11648/j.ajam.20150301.13

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@article{10.11648/j.ajam.20150301.13,
  author = {Felix Makanjuola Aderibigbe and Bosede Ojo and Kayode James Adebayo},
  title = {Numerical Experiment with the Construction of a Control Operator Applied in ECGM Algorithm},
  journal = {American Journal of Applied Mathematics},
  volume = {3},
  number = {1},
  pages = {8-13},
  doi = {10.11648/j.ajam.20150301.13},
  url = {https://doi.org/10.11648/j.ajam.20150301.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20150301.13},
  abstract = {In this paper, we constructed a control operator, G, which enables an Extended Conjugate Gradient Method (ECGM) to be employed in solving for the optimal control and trajectories of continuous time linear regulator problems. Similar operators constructed in the past by various authors have limited application. This call for the construction of the control operator that is aimed at taking care of any of the Mayer’s, Lagrange’s and Bolza’s cost form of linear regulator problems. The authors of this paper desire that, with the construction of the operator, one will circumvent the difficulties undergone using the classical methods and its application will further improve the result of the Extended Conjugate Gradient Method in solving this class of optimal control problem. The constructed Linear Control Operator is applied in ECGM algorithm to solve Continuous-Time Linear Regulator Problems with the convergence profile showing the efficiency of the operator.},
 year = {2015}
}

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TY  - JOUR
T1  - Numerical Experiment with the Construction of a Control Operator Applied in ECGM Algorithm
AU  - Felix Makanjuola Aderibigbe
AU  - Bosede Ojo
AU  - Kayode James Adebayo
Y1  - 2015/01/20
PY  - 2015
N1  - https://doi.org/10.11648/j.ajam.20150301.13
DO  - 10.11648/j.ajam.20150301.13
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 8
EP  - 13
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20150301.13
AB  - In this paper, we constructed a control operator, G, which enables an Extended Conjugate Gradient Method (ECGM) to be employed in solving for the optimal control and trajectories of continuous time linear regulator problems. Similar operators constructed in the past by various authors have limited application. This call for the construction of the control operator that is aimed at taking care of any of the Mayer’s, Lagrange’s and Bolza’s cost form of linear regulator problems. The authors of this paper desire that, with the construction of the operator, one will circumvent the difficulties undergone using the classical methods and its application will further improve the result of the Extended Conjugate Gradient Method in solving this class of optimal control problem. The constructed Linear Control Operator is applied in ECGM algorithm to solve Continuous-Time Linear Regulator Problems with the convergence profile showing the efficiency of the operator.
VL  - 3
IS  - 1
ER  -

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Author Information

Felix Makanjuola Aderibigbe

Department of Mathematical Sciences, Ekiti State University, Ado Ekiti, Nigeria
Bosede Ojo

Department of Mathematical Sciences, Ekiti State University, Ado Ekiti, Nigeria
Kayode James Adebayo

Department of Mathematical Sciences, Ekiti State University, Ado Ekiti, Nigeria

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Plain Text BibTeX RIS

APA Style

Felix Makanjuola Aderibigbe, Bosede Ojo, Kayode James Adebayo. (2015). Numerical Experiment with the Construction of a Control Operator Applied in ECGM Algorithm. American Journal of Applied Mathematics, 3(1), 8-13. https://doi.org/10.11648/j.ajam.20150301.13

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ACS Style

Felix Makanjuola Aderibigbe; Bosede Ojo; Kayode James Adebayo. Numerical Experiment with the Construction of a Control Operator Applied in ECGM Algorithm. Am. J. Appl. Math. 2015, 3(1), 8-13. doi: 10.11648/j.ajam.20150301.13

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AMA Style

Felix Makanjuola Aderibigbe, Bosede Ojo, Kayode James Adebayo. Numerical Experiment with the Construction of a Control Operator Applied in ECGM Algorithm. Am J Appl Math. 2015;3(1):8-13. doi: 10.11648/j.ajam.20150301.13

Copy | Download

@article{10.11648/j.ajam.20150301.13,
  author = {Felix Makanjuola Aderibigbe and Bosede Ojo and Kayode James Adebayo},
  title = {Numerical Experiment with the Construction of a Control Operator Applied in ECGM Algorithm},
  journal = {American Journal of Applied Mathematics},
  volume = {3},
  number = {1},
  pages = {8-13},
  doi = {10.11648/j.ajam.20150301.13},
  url = {https://doi.org/10.11648/j.ajam.20150301.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20150301.13},
  abstract = {In this paper, we constructed a control operator, G, which enables an Extended Conjugate Gradient Method (ECGM) to be employed in solving for the optimal control and trajectories of continuous time linear regulator problems. Similar operators constructed in the past by various authors have limited application. This call for the construction of the control operator that is aimed at taking care of any of the Mayer’s, Lagrange’s and Bolza’s cost form of linear regulator problems. The authors of this paper desire that, with the construction of the operator, one will circumvent the difficulties undergone using the classical methods and its application will further improve the result of the Extended Conjugate Gradient Method in solving this class of optimal control problem. The constructed Linear Control Operator is applied in ECGM algorithm to solve Continuous-Time Linear Regulator Problems with the convergence profile showing the efficiency of the operator.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Numerical Experiment with the Construction of a Control Operator Applied in ECGM Algorithm
AU  - Felix Makanjuola Aderibigbe
AU  - Bosede Ojo
AU  - Kayode James Adebayo
Y1  - 2015/01/20
PY  - 2015
N1  - https://doi.org/10.11648/j.ajam.20150301.13
DO  - 10.11648/j.ajam.20150301.13
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 8
EP  - 13
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20150301.13
AB  - In this paper, we constructed a control operator, G, which enables an Extended Conjugate Gradient Method (ECGM) to be employed in solving for the optimal control and trajectories of continuous time linear regulator problems. Similar operators constructed in the past by various authors have limited application. This call for the construction of the control operator that is aimed at taking care of any of the Mayer’s, Lagrange’s and Bolza’s cost form of linear regulator problems. The authors of this paper desire that, with the construction of the operator, one will circumvent the difficulties undergone using the classical methods and its application will further improve the result of the Extended Conjugate Gradient Method in solving this class of optimal control problem. The constructed Linear Control Operator is applied in ECGM algorithm to solve Continuous-Time Linear Regulator Problems with the convergence profile showing the efficiency of the operator.
VL  - 3
IS  - 1
ER  -

Copy | Download